Abstract

SUMMARY The purpose of this paper is to find a set of canonical elements to use within the framework of O¨ pik theory of close encounters of a small body with a planet (O¨ pik, Interplanetary Encounters, 1976). Since the small body travels along a planetocentric hyperbola during the close approach and O¨ pik formulas are valid, without approximations, only at collision, we derive a set of canonical elements for hyperbolic collision orbits (eccentricity e→1+, semi-major axis a fixed) and then we introduce the unperturbed velocity of the small body and the distance covered along the asymptote as a new canonically conjugate pair of orbital elements. An interesting result would be to get a canonical set containing the coordinates in the Target Plane (TP), useful for the analysis of the future encounters: in the last part we prove that this is not possible.